# Linear Equations In One Variable Questions

We provide linear equations in one variable practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on linear equations in one variable skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of linear equations in one variable Questions

Question NoQuestionsClass
1If ( frac{3 x+7}{5}=11, ) then ( x ) is equal to
A . 16
B . 15
c. -16
D. -15
8
2Find ( times ? )
( 2 x+3=7 )
8
316.
16. Solve the equation : 24-1 6x-2
Solve the equation : –
2x-1 6x-2
3
5
3
8
4Solve the following equation
( 7 y=77 )
8
5( A ) and ( B ) have 460 coins altogether. If ( frac{3}{4} ) of ( A^{prime} ) s number of coins is equal to ( frac{2}{5} ) of
B’s number of coins, find how many
coins must ( B ) give to ( A, ) so that they
both have equal number of coins.
A . 50
B. 70
c. 20
D. 90
8
6The numerator of a fraction is 5 less
than its denominator. If 3 is added to
the numerator and denominator both, the fraction becomes ( frac{4}{5} . ) Find the original fraction.
A ( cdot frac{1}{22} )
в. ( frac{17}{22} )
c. ( frac{17}{2} )
D. ( frac{7}{22} )
8
7Solve linear equation:
( frac{n}{2}-frac{3 n}{4}+frac{5 n}{6}=21 )
8
8DOUTONUL SIVUT Cyudulull.
6. The sum of two numbers, one of which
Sol. Let one of the number = r.
imes the other, is 50. Find two numbers.
8
9If ( 2(a-8 times 5)-2 times 7=3 times 1 times a+ )
( mathbf{7} times mathbf{4}-(mathbf{8} times mathbf{1} times mathbf{a}-mathbf{1}), ) find ( boldsymbol{a} )
A ( cdot frac{123}{8} )
B. ( frac{123}{7} )
c. ( frac{8}{123} )
D. ( frac{7}{123} )
8
10Three binders and four notebooks cost a
total if ( \$ 4.32 . ) One binder and five note-
books cost ( \$ 3.97 . ) What is the cost of
one notebook?
A . 0.50
B. 0.69
c. 0.72
D. 0.79
8
11If ( frac{x+3}{3}-frac{x-2}{2}=1, ) then find ( p, x+ )
( 3-(p+2)=5 )
8
12Given that ( -6 x=64-2(-x) )
calculate the value of ( x )
A . -8
B. -4
( c cdot 6 )
D. 16
8
13Solve ( frac{mathbf{7}}{mathbf{4}}-boldsymbol{p}=mathbf{1 1} )8
14The length of a rectangle is twice its width. If its perimeter is ( 54 mathrm{cm}, ) find its length.
( mathbf{A} cdot 18 mathrm{cm} )
B. ( 10 mathrm{cm} )
( mathrm{c} cdot 19 mathrm{cm} )
D. ( 15 mathrm{cm} )
8
15itics
11.
Linear Equations in One Variable
8. A number consists of two digits. The digit at ten’s place is
two times the digit at the unit’s place. The number formed
by reversing the digits, is 27 less than the original number.
Find the original number.
209
.
inen te
norte such that half of oneport is
1
8
16Solve ( boldsymbol{x}=frac{mathbf{4}}{mathbf{5}}(boldsymbol{x}+mathbf{1 0}) )8
17Two-third of a number is greater than
one-third of the number by 3. Find the
number
8
18If the solution of these equations. ( x-12=2 frac{2}{5} )8
19Sumeet thinks of a number and adds
( mathbf{4 0} )
( frac{40}{3} ) to it. He then multiplies the result by
3. The result now obtained is 8 times
the same number he thought of, what is the number?
A . 5
B. 6
c. 8
D. 7
8
207.
A number is such that it is as much greater than 112 as it is
less is than it. Find the number.
8
21If ( frac{5}{8} x+frac{2}{3}=frac{7}{12}, ) then ( frac{1}{2} x= )
A ( cdot frac{-1}{15} )
B. ( frac{-2}{15} )
c.
D.
8
22tiei denomulaULUI UUU UUU 13
19
5. On simplifing (
*)6*) weget . Find the
3 21
– X-
7 15
On simplifying
value of k.
et
Find the
8
23Solve the equation:
( frac{2 x}{3}=18 )
8
2410. Given that -0.3k + 2.1 = 0.4k, the value of k = ?8
25Solve ( 6 x+1=3(x-1)+7 ) for the
value of ( x )
8
2655. The sum of the ages of two
brothers, having a difference of
8 years between them, will
double after 10 years. What is
the ratio of the age of the younger
brother to that of the elder
brother?
(1) 10: 13 (2) 7:11
(3) 3:7 (4) 8:9
8
27Benny thinks of a number subtracts 18
from it and divides the difference by 3 The result is ( -4 . ) What is the number
8
28If you subtract ( frac{1}{2} ) from a number and multiply the result by ( frac{1}{2}, ) you get ( frac{1}{8} ) What is the number?
A ( cdot frac{3}{4} )
B. ( frac{1}{6} )
( c cdot frac{7}{4} )
D. ( frac{3}{5} )
8
29What should be added to ( 4 frac{8}{15} ) to get ( 9 frac{2}{5} ) ( ? )8
30The sum of the digits of a two digit number is ( 7 . ) If the digits are reversed, the new number decreased by 2 , equals twice the original number. Find the
number.
A . 25
B . 28
c. 43
D. 32
8
319.
Divide 300 into two parts so that half of one part may be less than the other by 48.
Sol I et one part of 300 beso other part will he (300-
8
32The value of ( frac{1}{4} x-5(q-x) ) ( -frac{3}{2}left(frac{1}{3}left(q-frac{x}{3}right)-frac{2}{9}left[x-frac{3}{4}left(q-frac{4 x}{5}right)right]right) ) is
A ( cdot frac{9 x}{5}+frac{q}{2} )
в. ( frac{9 x}{4}-frac{q}{2} )
c. ( frac{9 x}{5}-frac{q}{2} )
D. ( frac{11 x}{5}+2 q )
8
33A person bought a certain number of books for ( R s .80 . ) If he had bought 4
more books for the same sum, each
book would have cost ( R e .1 ) less. What is
the price of each book?
A . ( R s .10 )
в. Rs.
c. ( R s . )
D. Rs.
8
34One integer is two more than a second integer. The first integer added to four times the second is equal to ( 17 . ) Find the values of the two integers.
A .2 and 4
B. 3 and 5
c. 4 and 6
D. 1 and 3
8
35In the figure given, the measure in
degrees of ( angle A B C ) is ( 72^{circ} . ) Find the value
of ( boldsymbol{x} )
( mathbf{A} cdot 18^{circ} )
B. ( 24^{circ} )
( c cdot 27^{circ} )
( mathbf{D} cdot 30^{circ} )
8
36A number decreased by 30 is the same as 14 decreased by 3 times the number. Find the number.
A . 11
B. 9
c. 8
D. 12
8
37If you multiply a number by 3 and then add ( 40, ) the result is the same as if you
first add 17 and then multiply by 2 What is the result if you subtract 9 from
the number and then multiply by ( 4 ? )
A. -60
B. -72
c. -84
D . -108
8
38An aircraft pilot flies it at a distance of
( 800 k m ) with some average speed. He
could have saved 40 minutes by increasing the average speed of the aircraft by ( 40 k m / h . ) Find actual speed of the aircraft.
8
39( {3 x-2 leq 10 text { and } x ) belongs to natural numbers
Find the range of ( x )
8
40There is a number, the second digit of which is smaller than its first digit by 4 and if the number was divided by the
digits sum, the quotient would be ( 7 . ) Can you find the number?
A . 64
B. 46
c. 48
D. 33
E. 84
8
41Solution of the linear equation ( 3 x+ )
( 0 y+7=0 ) in two variables is of the
form
A ( cdotleft(frac{-7}{3}, mright) )
в. ( left(n, frac{-7}{3}right) )
c. ( left(0, frac{-7}{3}right) )
D. (-7,0)
8
421.
When a number is divided by 9, it is diminished by 56.
Then, the number is 47.
8
43Solve :
( frac{boldsymbol{x}+mathbf{2}}{mathbf{9}}=frac{boldsymbol{x}+mathbf{4}}{mathbf{1 1}} )
8
44Simplify ( frac{2 x+7}{5}-frac{3 x-11}{2}=frac{2 x+8}{3}-5 )8
45Solve the following:
( frac{4}{5}left(x+frac{5}{6}right)+frac{2}{3}left(x-frac{1}{4}right)=1 frac{1}{9} )
A ( cdot frac{9}{14} )
в. ( frac{5}{12} )
( c cdot frac{3}{11} )
D. ( frac{7}{11} )
8
46( frac{1}{10} ) of a rod is coloured red, ( frac{1}{20} ) orange ( frac{1}{30} ) yellow, ( frac{1}{40} ) green, ( frac{1}{50} ) blue, ( frac{1}{60} ) black
and the rest are violet. If the lenght of the violet portion is ( 12.08 mathrm{m} ), then what
is the lenght of the rod?
A. 16 m
B. 18 m
c. ( 20 mathrm{m} )
D. 30
8
47( 37-(3 x+5) geq 9 x-8(x-3) )8
48Solve
( mathbf{7}(boldsymbol{x}-mathbf{2})=mathbf{4 9} )
8
49A bird flies 1 kilometer in one minute.
Can you express the distance covered by the bird in terms of its flying time in
minutes? [use ( t ) for flying time in minutes
8
50Four fifth of a number is 4 more than
three fourth of the number. Find the
number.
8
51If Leah is 6 years older than Sue and
John is 5 years older than Leah and the total of their ages is ( 41 . ) Then how old is
Sue?
A . 8
B. 10
c. 14
D. 19
E . 21
8
52The numerator of the rational number is
less than its denominator by 3 . If the numerator becomes three times and
the denominator is increased by ( 20, ) the new number becomes ( frac{1}{8} . ) Find the original number.
8
53If ( a=b, ) then ( a+x= )
( mathbf{A} cdot a+x )
B. ( b x )
c. ( b-x )
D. ( b+x )
8
54Solve the following:
( frac{3 x}{4}-frac{1}{4}(x-20)=frac{x}{4}+32 )
A .112
в. 126
( c .108 )
D. 102
8
555.
Three numbers are in the ratio 1:2:3 and their sum is 120.
Find the numbers.
8
56Find the root of ( 2 x+frac{x}{2}=20 )8
57Evaluate:
( (x-2)+(x-3)+(x-9)=0 )
8
58Solve ( : 2 x=100 )8
59Check wheather the equality of the equation in maintained or not, by putting the value of the given variable written next to the equation below. ( boldsymbol{x}+mathbf{4}=mathbf{1 7} ) if ( boldsymbol{x}=mathbf{2} )
A. True
B. False
8
603t-22t+32
43
8
61Solve: ( frac{7}{10}-x=frac{3}{5} )8
62A man engaged a servant on the condition that he would pay him Rs. 90 and a turban after a service of one year.
He served only for nine months and received the turban and Rs. ( 65 . ) The
price of the turban is:
A . Rs. 25
B. Rs. 18.75
c. Rs. 10
D. Rs. 2.50
8
63If the angles of a triangle are in the ratio 2:3:4, then find the
difference between the greatest and smallest angles
8
64In solving an equation of the form ( a x+ )
( b=0 ) (a,b having only 1 as the common factor ( ), A ) made a mistake in copying ( b ) and ( operatorname{got} frac{7}{3} ) as the root whereas ( B ) made a mistake in copying ( a ) and ( operatorname{got} frac{8}{5} ) as the
root. The correct root is
( A cdot frac{7}{5} )
B. ( frac{3}{8} )
( c cdot frac{8}{3} )
D. ( frac{8}{5} )
8
65Solve the following equations and verify
( frac{2-y}{y+7}=frac{3}{5} )
8
66Sudhir’s present age is 5 more than three times the age of Viru, Anil’s age is half the age of Sudhir. If the ratio of the
sum of Sudhir’s and Viru’s age to three
times Anil’s age is ( 5: 6, ) then find Viru’s
age
8
67Solve:8 ( boldsymbol{x}+mathbf{5}>mathbf{1 3} )8
68Solve ( 8 t+5=2 t-31 ) for the value of ( t )8
69Four fifth of a number is more than
three-fourth of the same number by 40
Find the number.
8
70Find the value of ( x ) :
( frac{boldsymbol{x}-mathbf{5}}{mathbf{2}}-frac{boldsymbol{x}-mathbf{3}}{mathbf{5}}=frac{mathbf{1}}{mathbf{2}} )
8
71The number ( x ) was multiplied by 0.5 and
the product divided by ( 3 . ) The result was
squared and 1 added to it. The final result was ( 50 . ) What was the value of
number ( boldsymbol{x} ) ?
A .42
B. 30
( c cdot 24 )
D. 18
8
72Find the solution of ( 2 x-3>7 )8
73Solve the following equations.
( 4 x-3=2 x+1 )
8
74A rational number is such that when
you multiply it with ( frac{5}{2} ) and add ( frac{2}{3} ) to the
product, you get ( -frac{7}{12} . ) What is the
number?
A ( cdot-frac{4}{3} )
в. ( -frac{1}{2} )
( c cdot frac{4}{3} )
D. ( -frac{5}{3} )
8
75s. 6.5x+1958–32,5 = 6.5x+13+(13×720)
19.5x -32.5
(13x – 26
-= 6.5x +13+
5.
6.5x+
8
76Solve the equation. ( frac{3}{2 x}+frac{1}{x+1}=0 )8
77Solve the equation:
( mathbf{7} boldsymbol{x}-mathbf{9}=mathbf{1} 6 )
8
78Find 4 consecutive even numbers
whose sum is 356
8
798x
17
5x
6.
x+7-7-7-7
8
80Solve the following:
( frac{2 x-3}{2 x-1}=frac{3 x-1}{3 x+5} )
A ( cdot 1 frac{2}{3} )
в. ( 5 frac{2}{3} )
( c cdot_{7} frac{2}{3} )
D. ( 2 frac{2}{3} )
8
81If ( boldsymbol{x}=boldsymbol{2} boldsymbol{p}, ) then find the value of ( boldsymbol{p} ) from
the equation ( : 2(3 p+3)-frac{2}{5}(3+ )
( 4 x)=frac{9}{2} )
8
8211.
Form equations and solve the following statements:
(1) Thrice a number equals 60. What is the number?
(ii) 60 subtracted from a number gives 52. What is the
number?
(ii) Two numbers are in the ratio 5:8. If their sum is 130.
then find the numbers.
8
83The perimeter of a rectangular field is ( frac{3}{5} )
km. If the length of the field is twice its
width then find the area of the rectangle
( operatorname{in} m^{2} )
8
84f ( frac{14}{3}+left(frac{1}{2}right)left(x-frac{7}{3}right)=-frac{2 x}{3}, ) then the
value of ( x ) is:
A . -3
B. 3
( c cdot 6 )
D. – 6
8
85Divide 1000 into 2 parts such that 10
( % ) of one part equals ( 20 % ) of the other Find the bigger part.
A ( cdot frac{2000}{3} )
в. ( frac{1000}{3} )
c. ( frac{150}{3} )
D. None of the above
8
86Solve the following:
( frac{x-8}{5}=frac{x-12}{9} )
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
D. 3
8
87If ( p ) is added to ( -5, ) the result is ( 7 . ) Hence
( mathbf{3} boldsymbol{p}= )
( A cdot 6 )
B . 18
( c .36 )
D. 4
8
8811.
Two trains, one travelling 15 km/hr faster than the other,
leave the same station at the same time, one travelling east
and the other west. At the end of 6 hours they are 570 km
apart. What is the speed of each train?
8
89Solve for ( x ) in ( frac{2-(3 x-8)}{5-(4 x-9)}=frac{1}{2} )8
90Solve:
( 2-frac{7 x}{29}<frac{5}{3} )
8
91Solve:
( frac{91}{9}+2 a frac{13}{3}=169 )
8
92This month, Kami sold 70 figurines in 2 sizes. The large figurines sold for ( \$ 12 ) each, and the small figurines sold for ( \$ ) 8 each. The amount of money he
received from the sales of the large
figurines was equal to the amount of money he received from the sales of the
small figurines. How many large figurines did Kami sell this month?
A .20
B . 28
( c .35 )
D. 42
8
933.
If x +a=b, then x =
8
94If ( frac{50}{x}+3=13,50 x+3=13, ) then the
value of ( x ) is
( A cdot 2 )
B. 4
c. 5
D.
8
95Solve the following equations:
( frac{x}{2}-frac{1}{4}=frac{x}{3}+frac{1}{2} )
8
96A man left one-fourth of his money to his wife, two fifth to
his son and donated balance amount of 210000 to a
charitable fund. How much money did he have? How much
money was received by his wife and son separately?
14
Three numbers are in the rain 1.0.0
8
97Solve:
( frac{3 a-2}{7}-frac{a-2}{4}=2 )
8
98UUUUUUU
15. (1) Seven times a number is 49. What is the number?
(ii) One and halftimes of a number is 300, find the number
8
99Solve:
( frac{20 x}{3}=40 )
8
100Give first the step you will use to separate the variable and then solve the
equations ( frac{3 p}{10}=6 )
8
101Solve ( n=frac{3 n}{5}-1+frac{3 n}{5}-2 )8
102A man can row ( 9 frac{1}{3} k m p h ) in still water and finds that it takes him thrice as
much time to row up then as to row
down the same distance in the river.
Find the speed of the current.
8
103If ( frac{x-1}{3}=k ) and ( k=3, ) what is the value of ( x ? )
( A cdot 2 )
B. 4
c. 9
D. 10
8
104Solve:
( 5(4 x+1)-2-(5 x+3)=15 )
8
105Find ( x )
[
frac{mathbf{5} boldsymbol{x}-mathbf{4}}{mathbf{6}}=mathbf{4} boldsymbol{x}+mathbf{1}-frac{mathbf{3} boldsymbol{x}+mathbf{1 0}}{mathbf{2}}
]
8
106Find the value of ( x: )
( boldsymbol{x}^{2}+boldsymbol{p}^{2}=(boldsymbol{q}-boldsymbol{x})^{2} )
( ^{mathbf{A}} cdot frac{q^{2}-p^{2}}{2 q} )
в. ( frac{q^{2}-p^{2}}{2} )
( ^{mathrm{C}} cdot frac{q^{2}-p^{2}}{2 p} )
D. ( frac{p^{2}-q^{2}}{2 p} )
8
107ff ( 5(1-2 x)=15 ; ) evaluate ( x^{2}-3 x+ )
2
( A cdot 1 )
B. 4
( c .3 )
D. 6
8
108( 6 x-1=2 x+9 ) value of ( x )
A ( cdot 1 frac{1}{2} )
в. ( -2 frac{1}{2} )
c. ( frac{4}{10} )
D. ( _{2} frac{1}{2} )
8
1092.
The number which is subtracted from
to get
is
200
91
8
110For what value of ( x ) is ( frac{3 x+7}{5}=11 ) true?
A . -19
B. -16
c. 16
D. 19
8
111Hence, speed of boat in still water = 31.5 km/hr.
13. The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, find the numbers.
Sol. Let the first number be x. And, Second number = 2490-X
8
112f ( boldsymbol{x} times mathbf{1 6}=mathbf{2 5 6}, ) what is ( boldsymbol{x}=mathbf{?} )8
113Distance between two stations And B is 690 km Two cars
start simultaneously from A and B towards each other, and
the distance between them after 6 hours is 30 km. If the
speed of one car is less than the other by 10 km hr find the
speed of each car.
8
114The sum of three consecutive odd
numbers is ( 57 . ) Find the numbers.
A. 17,19 and 21
B. 19,15 and 25
c. 13,17 and 26
D. 21,13 and 29
8
115The length of a rectangle is ( 4 mathrm{cm} ) more than the breadth, and the perimeter is
( 11 mathrm{cm} ) more than the breadth. Find the
length and breadth of the rectangle.
A. ( l=1, b=7 mathrm{cm} )
В. ( l=6, b=3 mathrm{cm} )
c. ( l=7, b=8 mathrm{cm} )
8
116Solve:
( frac{x+2}{6}-left(frac{11-x}{3}-frac{1}{4}right)=frac{3 x-4}{12} )
8
1173x +1
5.
6.x-7
Solve for x:
2x +1
+5
8
118If –X=-, then x=
2′
8
119Solve for ( boldsymbol{x}: boldsymbol{3} boldsymbol{x}=frac{boldsymbol{2} mathbf{0}}{mathbf{7}}-boldsymbol{x} )
A ( cdot frac{2}{7} )
B.
( c cdot frac{4}{7} )
D.
8
120If ( frac{x}{2}-frac{x}{3}=frac{x}{4}+frac{1}{2}, ) then the value of ( x ) is
( A cdot 6 )
B . 24
( c .-6 )
( D )
8
121Solve the following equation using systematic method:
( boldsymbol{x}+mathbf{7}=mathbf{1 8} )
8
12210.
.. wel par = 300-108 = 132
Saurabh has 34 in the form of fifty paise and twenty-five paise coins. If the
of 50-paise coins, how many coins of each kind does he have?
coins. If the number of 25 paise coins be twice the num
Sol Let the number
8
123The sum of the digits of a two digit
number is 14. When we interchange the digits, it is found that the resulting new number is smaller than the original number by ( 18 . ) What is the original two digit number?
( mathbf{A} cdot 86 )
B. 68
c. 84
D. 48
8
1245.
If x= 5, then find the value of x + –
1
1+-
1+
8
125A number subtracted by 30 gives 14 subtracted by 3 times the number. Find
the number
8
126A steamer goes downstream from one point to another in 7
hours. It covers the same distance upstream in 8 hours. If
the speed of stream be 2 km/hr, find the speed of the steamer
in still water and the distance between the ports.
8
127If ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=boldsymbol{a}+boldsymbol{b} ) and ( boldsymbol{x}-frac{mathbf{1}}{boldsymbol{x}}=boldsymbol{a}-boldsymbol{b} )
then, which of the following is correct?
( mathbf{A} cdot a b=1 )
B. ( a b=2 )
( mathbf{c} cdot a+b=0 )
( mathbf{D} cdot a=b )
8
1285.
An equation altered if we multiply or divide both sides of
the equation by the same non-zero number.
8
129Solve and verify the result:
( 4 x+7=15 )
8
130Solve ( frac{mathbf{6 x}+mathbf{1}}{mathbf{3}}+mathbf{1}=frac{boldsymbol{x}-mathbf{3}}{mathbf{6}} )8
131When 19 is subtracted from the product of ( p ) and ( 4, ) the result is 17
Then, the value of ( p ) is
A ( cdot frac{-1}{9} )
B. ( frac{1}{9} )
( c .-9 )
D.
8
1324. If=b, then x =
then x =
8
133What is the value of ( a ) in terms ( b, ) if ( frac{a}{b}+ ) ( frac{a+2}{3 b}=frac{1}{4} ? )
A. ( frac{b+4}{2} )
в. ( frac{b-4}{2} )
c. ( frac{3 b-2}{4} )
D. ( frac{3 b+8}{16} )
E ( cdot frac{3 b-8}{16} )
8
134Andy is 27 years older than Ted, who is
38 years younger than Amy. In how many years will Andy be the same age as Amy is now?
A . 11
B. 12
c. 13
D. 10
8
135A number is 27 more than the number
obtained by reversing its digits. If its units and tens digits are ( x ) and ( y )
respectively, write the linear equation representing the above statement
8
1361.
Solve: 0.16(5x-2)=0.4x +7
8
1373.
1-(x-2)-[(x – 3)-(x – 1)]=0
8
138( -7 p-4(-3 p+2)= )
A. ( -19 p+8 )
B. ( 5 p+8 )
( mathbf{c} cdot-19 p-8 )
D. ( 5 p-8 )
8
1393 years ago, the average age of a family of 5 members was 17 years. ( A ) baby having been born, the average age of the family is same today. The present age of the baby is
A. 3 years
B. 2 years
c. ( 1 frac{1}{2} ) years
D. 1 years
8
140Solve: ( 8 x+frac{21}{4}=3 x+7 )
A ( cdot frac{2}{9} )
B. ( frac{7}{20} )
c. ( frac{6}{17} )
D. ( frac{4}{21} )
8
141Solve:
( frac{2 x+7}{5}-frac{3 x+11}{2}=frac{2 x+8}{3}-5 )
8
142Mathematics
12. Write the equations for the following statements:
() A number increased by 34 gives 86.
(i) Twice a number equals 20.
(ii) Halfof a number is 16.
(iv) Five times Romi’s age equals 100 years.
(v) Eight times a number added to 2 gives 60.
8
143For each graph given below, four linear equations are given. Out of these find the equation that represents the given
graph.Equations are
A) ( y=x )
B) ( boldsymbol{x}+boldsymbol{y}=mathbf{0} )
C) ( y=2 x )
D) ( 2+3 y=7 x )
8
144Solve the linear equation:
( 3 x+13=52 )
8
145The base of an isosceles triangle is ( frac{4}{3} ) ( mathrm{cm} . ) The perimeter of the triangle is
62
( frac{a}{15} mathrm{cm} . ) What is the length of either of remaining equal sides?
8
146Solve linear equation:
( frac{x-5}{3}=frac{x-3}{5} )
8
147Solve ( : mathbf{5}-frac{mathbf{2} mathbf{d}+mathbf{7}}{mathbf{9}}=mathbf{0} )
A . 19
B. 14
( c .9 )
D.
8
14851. A train running at an average
speed of 48 km/hr performs a
journey in 6 hours 30 minutes
How long would the same jour-
ney take it after crossing 180
kms, the speed was reduced to
33 km/hr?
(1) 7 hours 45 minutes
(2) 4 hours
(3) 3 hours
(4) 6 hours 45 minutes
8
149Solve:
( frac{x}{x+1}=frac{2}{3} )
8
150Find the value of ( boldsymbol{x}: frac{mathbf{4}}{mathbf{5}} boldsymbol{x}+mathbf{1 1}=frac{mathbf{1}}{mathbf{1 5}} )8
151The sum of two numbers is 45 and their
ratio is ( 7: 8 . ) Find the numbers.
8
152The product of two rational numbers is – 7. If one of the
number us -10, find the other.
8
153Check whether ( frac{1}{4} ) is a solution of the equation ( 3(x+1)-3(5-x)=2(5+x) )8
154Solve:
( left(1+frac{1}{x+1}right)left(1+frac{1}{x-1}right)=frac{7}{8} )
8
1556.
3.
A boat covers a certain distance downstream in 3 hours,
and it covers the same distance upstream in 5 hours. If the
speed of the boat in still water is 8 km/hr, then the speed of
the stream is
(a) 1 km/hr
(b) 1.5 km/hr
(c) 2 km/hr
(d) 3 km/hr
8
156Solve the following equation ( mathbf{2}(mathbf{2} boldsymbol{x}+mathbf{4})-mathbf{3}(boldsymbol{x}-mathbf{1})=mathbf{1 1} )8
157The product of two number is —
If one of the number
35
find the other.
(6)
(c) 75
(d)
who
8
15828
8.
The product of two numbers is –
. If one of the numbers
, then the other number is _
Nlur
wIT
8
159Solve: ( frac{3 x+5}{2 x+7}=5 )8
160Find the solution set of ( frac{3}{5} x-frac{2 x-1}{3}> )
1
8
161Three collinear points ( A, B ) and ( C ) ares
such that point ( B ) is between points ( A ) and ( C . ) The distance from ( A ) to ( B ) is 8
more than 4 times the distance from ( B )
to ( C ) and the distance from ( A ) to ( C ) is 5
times the distance from ( B ) to ( C . ) What is
the distance from ( boldsymbol{A} ) to ( boldsymbol{C} ) ?
A .4
B . 20
c. 16
D. 24
8
162solve
( mathbf{3} boldsymbol{x}=mathbf{3} mathbf{3} mathbf{6}+mathbf{2} mathbf{4} mathbf{3} )
8
163Solve each of the following equations and also verify your solution:
( frac{7}{x}+35=frac{1}{10} )
8
164Litlal isur
SUV NE BE IN
un equation is called
3.
2x+1
Find the solution of
37-1
8
165Solve the following equation: If ( 14 y- ) ( 8=13 ) and ( y=frac{3}{q}, ) then ( q ) is
A . 3
B.
( c cdot 2 )
D.
8
166Set up equations and solve them to find the unknown numbers in the following
cases:
lbenhal thinks of a number. If she adds
19 to it divides the sum by 5, she will get
8
8
167A man’s age is six times the age of his son. In six years, the father’s age will be three times of the son’s age. The age of
the father and the son are respectively:
A. 18 years and 3 years
B. 30 years and 5 years
c. 24 years and 4 years
D. 42 years and 7 years
8
16810.
The sum of three consecutive multiples of 11 is 363. Find
these multiples.
8
1693
3
5.
3m= 5m –
17
8
170Ashok went to a casino to play a card game. In each round, he happened to double the amount with himself and in
each round he gave Rs. ( x ) to his friend. At
the end of three rounds, he was left with
no money. If the amount he gave to his
friend in each round was Rs. 20 more
than the amount he started with, find
the amount (in Rs.) that he started with
A. 110
в. 120
( c .130 )
D. 140
8
171Check whether the value given in the brackets is a solution to the given equation or not:
8
1723t-2
2t+3
+
-=tt
8
173Solve: ( 14 y-8=13 )
A . 1.9
в. 1.5
c. ( 1 . )
D. 1.6
8
1747.
The
The volume of water in a tank is twice of that in the other. I
we draw out 25 litres from the first and add it to the other,
the volumes of the water in each tank will be the same. Find
the volume of water in each tank.
8
175The difference between the ages of a
woman and her son is 19 years and the
sum of their ages is 37 years. Find the age of the son.
8
176State whether the given statement is true or false.
If ( boldsymbol{p}^{1-2 x} times sqrt{boldsymbol{p}}=boldsymbol{q}^{1-2 x} times sqrt{boldsymbol{q}} ; boldsymbol{p} neq boldsymbol{q} ) then
value of ( boldsymbol{x} ) is ( frac{mathbf{3}}{mathbf{4}} )
A. True
B. False
8
1773
2
2
5
6
2.
The speed of car is 54-km per hour. What is the distance
travelled in 3 hours and 33 minutes
A mother and her to doughtore got room on
8
178Solve the given equation for ( y: ) ( frac{1-9 y}{19-3 y}=frac{5}{8} )
A ( -frac{66}{103} )
в. ( frac{38}{73} )
( c cdot-frac{87}{57} )
D. None of these
8
179The value of ( x ) is ( 3 x+4=13 )
A . 3
B. 4
c. 5
D. None of these
8
1802. = (x +10)8
181How much money does Trishika have?
A . ( R s .125 )
B. Rs.110
c. ( R s .115 )
D. Rs.120
8
1821.
A man has a certain number of 5 rupee coins, 2- rupee
coins, 1-rupee coins and 50 paise coins. The number of
5- rupee coins is 7 less than 2-rupee coins, the number of
1-rupee coins is 15 more than 5-rupee coins and the number
of 50 paise coins is twice the number of 2-rupee coins. Ifa
man has 198 in all, find the number of coins of each
denomination.
8
183Runs scored by Rahul in a match are 38
more than that faced by Virat. If together they have scored 144 runs and
the runs scored by Rahul are 18 more
than those faced by Virat. Find the number of runs scored by Rahul
8
1845. f3+x+639
– +x+

5
22
-125
462
7125, then x is
then x is
Ol=
6
(6)
=
8
185Solve:
( frac{boldsymbol{x}+mathbf{5}}{mathbf{5}}=mathbf{6} )
8
1861. Solve for y: 431+1) – (5+2)=y-1 om8
187When ( x=2, ) the value of the
expression ( 4 x^{2}+frac{9}{x^{2}}-12 ) is:
A ( cdot frac{25}{4} )
в. ( frac{-4}{25} )
c. ( frac{4}{25} )
D. ( frac{-25}{4} )
8
188Set up an equation in the following
cases:
Irfan says that he has 7 marbles more than five times the marbles Pramit has.
Irfan has 37 marbles. (Let ( m ) to be the
number of Pramit’s marbles.)
8
189Solve the following equation:
( 7 x-5=2 x )
8
190Solve :
( frac{x}{2}-frac{1}{5}=frac{x}{3}+frac{1}{4} )
8
191Solve:
( frac{1}{3}(x-2)+frac{1}{4}(x+3)=frac{1}{5} )
8
192value ok.
The sum of two rational numbers is
If one of the
-k
than the other, number is
. Find the
number is
value of k.
8
193Solve:
( frac{65}{12}-x=frac{33}{-4} )
8
194Solve the linear equation:
( mathbf{1 5}(boldsymbol{y}-mathbf{4})-mathbf{2}(boldsymbol{y}-mathbf{9})+mathbf{5}(boldsymbol{y}+mathbf{6})=mathbf{0} )
A ( y=frac{1}{7} )
B. ( y=frac{3}{5} )
c. ( y=frac{5}{2} )
D. ( y=frac{2}{3} )
8
195Solve
( frac{5}{6} x+frac{3}{8} x=2+frac{1}{3} x )
8
196Two numbers are in the ratio ( 3: 4 . ) If
their LCM is 180 , find the numbers.
8
197If ( y=f(x)=frac{x+2}{x-1}, ) than it is incorrect
to say:
A. ( x=frac{y+2}{y-1} )
B. ( f(0)=-2 )
c. ( f(1)=0 )
D. ( f(-2)=0 )
E . ( f(y)=x )
8
198The ratio of the mango trees and orange
trees is ( 7: 9 . ) If 5 mango trees and 5
orange trees were planted in addition
the ratio would be ( 27: 34 . ) Find the
number of mango trees.
8
1994.
Simplify the following linear equations, then solve them:
7y-2_3+ 7y
(1) 5y-1 4+5y
11 – 2
a + 2 a +1 a +10
+
cm) 0,*-5(0.2x – 3) =3*
8
200The prices of table and chair are in the
ratio of ( 25: 6 . ) If table costs Rs. 950
more than chair, then cost of two chairs
is
A . Rs. 300
B. Rs. 600
c. Rs. 900
D. Rs. 1200
8
201A man leaves a town at 8 a.m. on his
bicycle moving at ( 10 mathrm{km} / mathrm{hr} ). Another
man leaves the same town at 9 a.m. on
his scooter moving at ( 30 mathrm{km} / mathrm{hr} . ) At what time does he overtake the man on the
bicycle?
A. 8.30 a.m.
B. 9 a.m.
c. 9.30 a.m.
D. 10 am
8
202If ( 4^{x}-4^{x-1}=24, ) then ( (2 x)^{x} ) equals
A . 25
в. 125
( c cdot sqrt{5} )
( mathbf{D} cdot 25 sqrt{5} )
8
203.. Distance covered on foot = 7 km.
12. A motor boat covers a certain distance downstream in a river in five hours. It covers the same distance upstream in five as
half hours. The speed of water is 1.5 km/hr. Find the speed of the boat in still water?
Sol. Let speed of boat in still water = x km/hr and speed of water = 1.5 km/hr
8
204A number is subtracted from ( 72 . ) The
new number is divided by 6 to give 10
Find the number.
8
205Oranges are to be transferred from larger boxes to smaller boxes. When a larger box is emptied, the oranges from it fill 3 smaller boxes and still 7 oranges
are left. If the number of oranges in a
small box are taken to be ( x ), then what
is the number of oranges in the larger
box
8
206Write equations for the following
statements:
If you take away 6 from 6 times ( y, ) you
( operatorname{get} 60 )
8
207In a shooting competition a marksman receives 50 paise if he hits the mark and pays 20 paise if he misses it. He tried 60 shots and was paid Rs. 1.30 How many times did he hit the mark?
A . 19
B. 22
( c cdot 18 )
D. 21
8
208Check whether the values given in the
brackets are the solutions of the
corresponding equation:
( boldsymbol{x}+mathbf{5}=mathbf{1 9} ;(boldsymbol{x}=mathbf{4}) )
8
209Solve ( mathbf{5} boldsymbol{x}+frac{mathbf{2 7}}{mathbf{3}}=mathbf{0} )8
210solve :
( frac{p}{3}+frac{p}{4}=55-frac{p+40}{5} )
8
211What number divided by two is equal to that same number minus ( 15 ? )
A . 30
B. 34
c. 15
D. 60
8
212When seventh part of a number is increased by 2 and fifth
part of the same number is decreased by 4, they become
equal. Find the number.
8
213The solution of the equation ( 10-3 y=1 ) is
( y= )
A. 0
B. 1
( c cdot 2 )
D. 3
8
214( times frac{1}{10}=frac{1}{30} times frac{1}{40} ; ) the value of ( x ) is
A ( cdot frac{1}{120} )
B. 400
c. 120
D. ( frac{1}{400} )
8
215Tanya’s grandfather was 8 times older to her 16 years ago. He would be 3 times
of her age 8 years from now. Eight years ago, what was the ratio of tanya’s age to that of her grandfather?
A .1: 2
B. 1: 5
c. 3: 8
D. 11: 53
8
216LOUICU UUELITOIMICOTICO
In a college of 300 students every student reads 5
newspapers and every newspaper is read by 60 students.
The number of newpapers is
(1998 – 2 Marks)
(a) at least 30
(b) at most 20
(c) exactly 25
(d) none of these
8
21713.
A rational number is such that when you multiply it by
to the product, you get –
5. What is the
number?
8
2186.
If the side of chess board is smaller than its perimeter by 24
cm, then find the side of the chess board.
L
e
mich arestar than 112 as it is
8
219( ln frac{a}{8}+frac{a}{4}=6 ) the value of a is
A. 122
B. -16
c. 16
D.
8
220The ratio of ( j ) to ( k ) to ( l ) to ( m ) to ( p ) is 5 to 4 to 3 to 2 to ( 1 . ) If ( j=60, ) what is the
value of ( m ? )
( A cdot 8 )
B. 12
c. 24
D. 55
8
2212 years back the age of Sushil’s father was 7 times Sushil’s age then. If the
sum of their present age is 36 years,
what is the age of Sushil’s father at
present in years?
A .28
B . 30
c. 40
D. None of these
8
222( frac{x-1}{2 x+1}+frac{2 x+1}{x-1}=frac{5}{2} )8
22362. 25 litres of salt solution con-
tains 6% salt. How many li-
tres of water must be added so
as to get a resultant solution
containing 5% salt ?
(1) 4 litres (2) 5 litres
(3) 6 litres (4) 8 litres
8
224The solution of the equation ( 1.5 y- ) ( mathbf{7}=mathbf{0 . 5 y} ) is
( A cdot 7 )
в. -7
( c .3 .5 )
D. – 3.5
8
225Here is an equation ( 2(x+12)=4 x-6 )
Solve the equation by first dividing both sides by 2
8
226A positive number is 5 times another
number. If 21 added to both the
numbers, then one of the new numbers
becomes twice the other new number.
What are the numbers?
8
227A number is added to ( 15 . ) The new
number is multiplied by 3 to give 60 Find the number.
8
228Solve the following equation. ( 2 x-frac{1}{3}=frac{1}{5}-x )8
229Solve:
( frac{3(y-5)}{4}-4 y=3-frac{(y-3)}{2} )
8
230The solution of the equation 2x + 5 = 0 is8
231f ( 3 x+8=17 ) find the value of ( x )8
232Solve: ( frac{1}{3(x-1)}-frac{1}{4(x-2)}=1 )8
233Find the solution of the given equation:
( frac{[9 x-(3+4 x)]}{[2 x-(7-5 x)]}=frac{6}{7} )
8
234Solve ( frac{mathbf{3}}{mathbf{1 1}}+boldsymbol{x}=frac{mathbf{9}}{mathbf{1 1}} ) for the value of ( boldsymbol{x} )8
235Solve the equation:
( mathbf{5} boldsymbol{x}+mathbf{2} frac{mathbf{3}}{mathbf{5}}=mathbf{9}-frac{mathbf{4}}{mathbf{5}} boldsymbol{x} )
8
236solve ( : boldsymbol{y}-frac{boldsymbol{y}}{mathbf{2}}=frac{mathbf{7}}{mathbf{4}}-frac{boldsymbol{y}}{boldsymbol{4}}-frac{boldsymbol{y}}{boldsymbol{4}} )8
2374.
Solve the following:
8
238Find the value of ( p: )
( (p-3)(p+3)-p(p+8)=15 )
( mathbf{A} cdot mathbf{3} )
B. -3
c. ( frac{-1}{3} )
D.
8
23910. Solve for x
(1) 12 (3 – x) = 48
(ii) 2x + (x+1)+(x + 2)=103
8
240Solve each of the following equations and check your answers: ( boldsymbol{x}-mathbf{3}=mathbf{5} )8
241The value of ( m ) for which the
expressions ( 2 m-5 ) and ( 5 m-11 )
become equal is
A . -2
B. 0
( c cdot 2 )
D. –
8
2427.
Find three even consecutive integers whose sum is 90.
8
243Solve the following equation: ( frac{5}{2} x=frac{25}{4} )8
244Given that ( 5 x-2(6+7 x)=15, ) the
value of ( x ) is
A ( cdot 1 frac{13}{14} )
B. ( 1 frac{8}{19} )
( c cdot frac{1}{3} )
D. – 3
8
245Twice the number is 24 greater than its half. Find the number.8
246Find the zeroes of the polynomial ( frac{1}{7} x- ) ( frac{2}{7} )8
2472.
Solve forx: 2+2x-3_3x+4
– 2x+3x+2
8
248Find the number, one third of which is 4
more than 5
A .27
B . 23
c. 25
D. 29
8
249Solve: ( frac{mathbf{3}}{boldsymbol{x}+mathbf{3}}=frac{mathbf{5}}{boldsymbol{x}+mathbf{2}} )8
250n ( 6(2 a-1)+8=14 );the value of ‘ ( a ) ‘ is
A . -1
в. ( _{3} frac{1}{12} )
c. ( _{1} frac{1}{12} )
D. +1
8
251If ( 12+frac{3 sqrt{x-5}}{2}=18, ) find the value of
( x ? )
A . 21
B . 20
( c cdot 26 )
D. 18
8
252muy uuys UI Te Work
12. For what value of x is the perimeter of shape 77 cm?
(x+1)
(x + 1)
(x+2)
(2x + 1)
(2x + 2)
8
253If ( 5 x+6=10, ) what is the value of
( 10 x+3 ? )
( A cdot 4 )
B. 9
( c cdot 11 )
D. 20
8
254Solve the following linear equations. If
( x+7-frac{8 x}{3}=frac{17}{6}-frac{5 x}{2}, ) then ( x ) is equal
to
A . -5
B. – 1
( c cdot 2 )
( D )
8
255Jim has a triangular shelf system that
attaches to his showerhead. The total
height of the system is 18 inches, and
there are three parallel shelves
as shown above. What is the maximum
height, in inches, of a shampoo bottle
that can stand upright on the middle shelf?
8
256Solve: ( 2.25 x-125=3 x+3.75 )8
257Solve:
( boldsymbol{x}+mathbf{7}-frac{mathbf{8} boldsymbol{x}}{mathbf{3}}=frac{mathbf{1 7} boldsymbol{x}}{mathbf{6}}-frac{mathbf{5} boldsymbol{x}}{mathbf{8}} )
8
258Solve ( frac{3 a-2}{3}+frac{2 a+3}{2}=a+frac{7}{6} )8
259Find the value of ( boldsymbol{x}: ) ( boldsymbol{x}-left[mathbf{2} boldsymbol{x}-frac{mathbf{3} boldsymbol{x}-mathbf{4}}{mathbf{7}}right]=frac{mathbf{4} boldsymbol{x}-mathbf{2 7}}{mathbf{3}}-mathbf{3} )8
260Solve the following equation and check
( boldsymbol{x}+(boldsymbol{x}+mathbf{2})=(boldsymbol{x}+mathbf{4})+mathbf{3 1} )
8
261Solve ( -mathbf{7}(mathbf{2}+boldsymbol{x})=mathbf{8} mathbf{7} )8
262Solve for ( boldsymbol{a}: boldsymbol{4} boldsymbol{a}-boldsymbol{9}>boldsymbol{9} boldsymbol{a}-boldsymbol{2} boldsymbol{4} )
( mathbf{A} cdot a>3 )
B. ( a<3 )
c. ( a<-3 )
D. ( a<9 )
8
263Pradeep is a Section Chief for an electric utility company. The employees in his section cut down tall trees or
climb poles. Pradeep recently reported the following information to the
management of the utility Out of 100 employees in my section, 55 can cut tall trees, 50 can climb poles, 1
can do both, 6 can’t do any of the two. Is this information correct?
8
264( A ) earns ( 800 R s . ) more than ( B . ) They
both save together ( 3,200 R s . ) which is
one-fourth of ( boldsymbol{A}^{prime} ) s salary plus one-sixth
of ( B^{prime} ) s salary. Find out their total monthly expenditure.
A. Rs. 12,000
B. Rs. 15,000
c. Rs. 10,000
D. Rs. 17,000
8
265The sum of two numbers is ( 184 . ) If one-
third of the one exceeds one-seventh of
the other by ( 8, ) find the smaller number.
8
266What is the number when it
is increased by ( 10 % ) becomes ( 88 ? )
8
267Prove that:
( 2 m+7=9 )
8
26872. A boat goes 12 km downstream
and comes back to the starting
point in 3 hours. If the speed of
the current is 3 km/hr, then the
speed (in km/hr) of the boat in
still water is
(1) 12 (2) 9
(3) 8
(4) 6
8
269If ( frac{a}{8}+frac{a}{4}=6, ) the value of ( a ) is
A . 122
B. -16
c. 16
D.
8
270( frac{3 x-2}{5}=4-left(frac{x+2}{3}right), ) find ( x )8
271Solve the following equation ( -4(2- )
( boldsymbol{x})=mathbf{9} )
8
272Solve
( left|boldsymbol{x}+frac{1}{3}right|>frac{8}{3} )
8
273Two numbers are in the ratio ( 1 frac{1}{2}: 2 frac{2}{3} )
But if each number is increased by 15 then the ratio becomes ( 1 frac{2}{3}: 2 frac{1}{2} . ) The
numbers are
( mathbf{A} cdot 27,42 )
B . 36,48
c. 27,48
D. 27,36
8
2748.
When seventh part of a number is increased by 2 and fifth
part of the same number is decreased by 4, they become
equal. Find the number.
Solve the following ut:
8
2751.
Solve the following equations:
(i) *-5-1-3-23
5x+3
45 1 – 2
8
276Find ( f: )
( mathbf{0 . 2 5}[mathbf{4 f}-mathbf{3}]=mathbf{0 . 0 5}[mathbf{1 0} boldsymbol{f}-mathbf{9}] )
8
277Dhoni scored twice as many runs as
Sehwag. Together they scored two runs less than double century. How many
runs did each of them score?
8
278A cart is running at an average speed of ( 3.6 k m / h r . ) How much time will it take
to go 380 metres?
8
279Solve the following equation and check
( 2 x-1=14-x )
8
280#NAME?8
281If the value of ( y ) is 3 then find value of ( x ) if ( frac{1}{x}+frac{1}{y}=frac{5}{6} )8
282( boldsymbol{x}+frac{mathbf{4}}{mathbf{3}}=mathbf{3} frac{mathbf{1}}{mathbf{2}} )8
283f ( 2 x-1=14-x ), then ( x= )
( mathbf{A} cdot mathbf{1} )
B . 2
c. 9
D.
8
284Last week Raul worked 11 more hours
than Angelica. If they worked a combined total of 59 hours, how many hours did Angelica work last week?
A .24
B. 35
c. 40
D. 48
8
285At present Pooja is 21 years younger to her mother. 6 years from now, Pooja will be half her mother’s age then. How old is Pooja’s mother at present?
A. 36 years
B. 40 years
c. 42 years
D. 45 years
8
28617. 17 / 3 = 2 / then y = ?
17.
then y = ?
dicito
T
8
28734
Mathematic
11. A boy covers a distance of 25 km in 4 hours partly on foot at the rate of 3.5 km/hr and partly on cycle at 9 km/hr. Find th
distance covered on foot.
Sol at the distance covered on foot he x km.
8
2886.
What number should be added to
get
11
30
(a) zo
8
289If ( x % ) of 200 is ( 10, ) then the value of ( x ) is
A . 10
B. 2
( c .5 )
D. none of the above.
8
290The total salary drawn by 3 watchmen, A, B and C is Rs. 1720. They spend 70%, ( 60 % ) and ( 50 % ) respectively from their salaries. If the balance with them are
into Ratio ( 1: 2: 3, ) what is the salary of
each?
A. A Rs. 300; B Rs. 500; C- Rs. 700
B. A Rs. 200; B Rs. 300; C-Rs. 650
c. A Rs. 100; B Rs. 300; C-Rs. 600
D. A Rs. 400; B Rs. 600; C- Rs. 720
8
291If ( 9-7 x=5-3 x, ) then the value of ( x )
is
A . 0
B. ( frac{1}{4} )
( c cdot frac{1}{2} )
D.
8
292Solve:
( frac{1}{5}left(frac{1}{3 x}-5right)=frac{1}{3}left(3-frac{1}{x}right) )
8
293Find the value of ( s: )
( s(3 s-7)-3 s(s-8)=9 )
A ( cdot frac{17}{9} )
в. ( frac{9}{17} )
( c cdot frac{-9}{17} )
D. ( frac{-17}{9} )
8
2948.
Find a number whose fifth part increased by 30 is equal to
its fourth part decreased by 30.
8
295A purse has only one rupee and two rupee coins in it. The number of two rupee coins is one third the number of
one rupee coins. If the purse has Rs. 115. Find the number of two rupee
coins.
A . 20
B . 23
c. 18
D. 25
8
296( A B ) is a segment. The point ( P ) is on the perpendicular bisector of segment AB such that length of AP exceeds length of AB by ( 7 mathrm{cm} . ) If the perimeter of ( Delta A B P ) is ( 38 mathrm{cm} . ) Find the sides of ( Delta A B P )
( mathbf{A} .5 mathrm{cm}, 12 mathrm{cm} ) and ( 19 mathrm{cm} )
B. ( 8 mathrm{cm}, 15 mathrm{cm} ) and ( 15 mathrm{cm} )
c. ( 2 mathrm{cm}, 17 mathrm{cm} ) and ( 11 mathrm{cm} )
D. ( 6 mathrm{cm}, 14 mathrm{cm} ) and ( 18 mathrm{cm} )
8
2975.
If 5 less than a number is 72 then the number is
2n-1)
8
298Find two consecutive natural numbers
whose sum is 63
A. 31 and 36
B. 30 and 32
c. 31 and 32
D. 54 and 32
8
2994.
– 18
The root of equation –
2z-3 3z–2
(a) – 7/2
(b) 7/2
(c) 3/2
(d) -3/2
or het
8
300A lending library has a fixed charge for first 3 days and an additional charges for each day there after. Sarika paid Rs.
27 for a book kept for 7 days while Sonali paid Rs.21 for the book she kept for 5 days. find the fixed charge and the additional charge per day.
8
30158. The simplified form of
1 1 ax
x+a+x+bx+c * x3 + ax2
8
302Shobos mothers present age is six times Shobos present age. Shobos age five years from now will be one third of
his mothers present age. What are their resent ages?
A. Shobos age: 5 years; Shobos mothers age: 30 years
B. Shobos age: 4 years; Shobos mothers age: 24 years
c. Shobos age: 10 years; shobos mothers age: 60 years
D. Shobos age: 1 years; shobos mothers age: 6 years
8
3037.
Solution of 0.18(5x-4)=0.5x +0.8 is
quotion intol
A
8
304The solution of ( frac{x-5}{2}-frac{x-3}{5}=frac{1}{2} )
is
( mathbf{A} cdot x=7 )
B. ( x=9 )
c. ( x=8 )
D. ( x=5 )
8
3053. Solve for y: }(32+1) -(52+2)=y-18
3061.
8x +4=3 (x-1)+7
8
and visit three temples one by one. At
each temple, she offers one half of the flowers from the basket. If she is left
with 3 flowers at the end, find the number of flowers she had in the
beginning.
8
308Check wheather the equality of the equation in maintained or not, by putting the value of the given variable written next to the equation below. ( 4 y-3=17 ) if ( y=2 )
A. True
B. False
8
30914. Find the number ifone-fourth of which is 8 more than 5.8
310Solve: ( 3 n+7=1 )8
311If ( a=-6 ) and ( b=7, ) then ( 4 a(3 b+5)+ )
( mathbf{2 b}=mathbf{?} )
A . 638
в. 624
( c .610 )
D. -610
E . -638
8
312Solve the following equation: ( 3^{x-1} times )
( mathbf{5}^{2 y-3}=225 )
A ( cdot x=3, y=frac{5}{2} )
в. ( _{x}=-3, y=frac{5}{2} )
c. ( _{x}=3, y=frac{-5}{2} )
D. None of the above
8
313individually!
14. On a winter day the temperature at a place in Himachal
Pradesh was -16° C. Convert it in degree Fahrenheit (°F)
by using the formula. –
F-32
Shnini has to cut out circler of die
8
314In a particular week the average
number of people visited the museum is ( 70 . ) If we exclude the holidays then the average number is increased by 28 Further if we exclude the day which the maximum of 210 visitors visited the
museum, then the average become 40 Find the no of holidays in the week
8
3153.
X-4 2x-3 5x-32 X +9
Solve, 3 + 35 = 9 – 28
11
8
316Find the value of ( x ).
( sqrt{mathbf{3}} boldsymbol{x}-mathbf{2}=mathbf{2} sqrt{mathbf{3}}+mathbf{4} )
( mathbf{A} cdot x=2(1+sqrt{3}) )
в. ( x=(1+2 sqrt{3} )
c. ( x=3(2+sqrt{2}) )
D. ( x=-2(3+sqrt{3}) )
8
317Find the first three terms in the
expansion of :
( frac{1}{(1+x)^{2} sqrt{1+4 x}} )
8
3186.
13500 are to be distributed among Salma, Kiran and Jenifer
in such a way that Salma gets 1000 more than Kiran and
Jenifer gets *500 more than Kiran. Find the money received
by Jenifer.
8
319Value of ( n ) that satisfies the equation ( frac{7}{8}(n-6)=frac{21}{2} ) is
A . 28
B. 18
c. 14
D. 22
8
3201.
=0, then x =
If + 1
x+1 x+4
(a) 21
(6) – 2 / 2
(c) 3 2
(d)
– 3
8
321Find the value:
1. ( 7 x-5=2 x )
2. ( 5 x-12=2 x-6 )
3. ( 7 p-3=3 p+8 )
8
322A can do a piece of work in 10 days, and
B can do the same work in 20 days. With the help of ( C ), they finished the work in 4 days. ( C ) can do the work in how many days, working alone?
8
3233.
If two-thirds of a number is greater than one-fourth of the
number by 5, find the number.
A man left one fourth ofhis money to his wife two fifth to
8
324Solve for ( x: frac{1}{3}=frac{sqrt{x}}{2} )
A ( cdot frac{7}{9} )
в. ( frac{5}{9} )
( c cdot frac{4}{9} )
D. ( frac{2}{9} )
8
3250.
0.0
15
8.
An equation involving only
a linear equation.
variable is called
8
326Solve the linear equation:
( boldsymbol{m}+mathbf{1 0}=mathbf{1 6} )
8
3276.
Solution of the equation – 3(p-1)-2 is
10
8
3282.
Solve the equation:
+ 2t3t_5+ 11ta to more
002 3 4 6 12
–+—–

+

+4
8
3292.
If 5x = 5, then x =
8
330Solve ( frac{x}{5}=12 ) for the value of ( x )8
3313(x – 5)_2
13. Solve
8
332Pipe M and N running together can fill a cistern in 6 minutes. If ( mathrm{M} ) takes 5
minutes less than ( mathrm{N} ) to fill the cistern,
then the time in which ( mathrm{N} ) alone can fill
the cistern will be
A . 15 min
B. 20 min
( c .25 ) min
D. 10 min
8
3339.
0.25(4f – 3) = 0.05(10f-9)
8
334Find a positive value of ( x ) for which the
given equation is satisfied:
( frac{y^{2}+4}{3 y^{2}+7}=frac{1}{2} )
8
335Solve:
( frac{x}{2}-frac{x}{3}-1=4 )
8
336Solve ( : 3 x+11=6 x-13 )8
3375.
4(3p+2) – 5(6p-1)=2(p – 8)–6(7p-4)
F1
8
338If ( boldsymbol{m}=mathbf{2}(mathbf{1 5}-mathbf{4} boldsymbol{x}), boldsymbol{n}=frac{mathbf{5} boldsymbol{x}+mathbf{3}}{mathbf{2}} ) and
( boldsymbol{m}: boldsymbol{n}=boldsymbol{2}: boldsymbol{3} ; ) find ( boldsymbol{n} )
( mathbf{A} cdot n=2 )
В . ( n=7 )
c. ( n=9 )
D. ( n=12 )
8
339If ( 0.6 x+0.8=0.28 x+1.16, ) then ( x= )
A ( cdot x=frac{6}{7} )
в. ( x=frac{9}{8} )
c. ( x=frac{11}{2} )
D. ( x=frac{13}{5} )
8
3402d+7
9.
Find the value of difs-
-=0
is
8
341( frac{boldsymbol{x}+boldsymbol{4}}{boldsymbol{2}}+frac{boldsymbol{x}-boldsymbol{3}}{boldsymbol{3}}=frac{boldsymbol{x}+boldsymbol{2}}{boldsymbol{4}}+frac{boldsymbol{x}+boldsymbol{3}}{boldsymbol{5}}, ) find
the value of ( x )
8
342Solve: ( 6 x-1=2 x+9 )
A ( cdot 1 frac{1}{2} )
в. ( -2 frac{1}{2} )
c. ( frac{4}{10} )
D. ( _{2} frac{1}{2} )
8
343( 3 x-1=9-2 x )8

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